Strong spin-orbit coupling and magnetism in (111) (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35})$/SrTiO$_3$.

Strong correlations, multiple lattice degrees of freedom, and the ease of doping make complex oxides a source of great research interest. Complex oxide heterointerfaces break inversion symmetry and can host a two dimensional carrier gas, which can display a variety of coexisting and competing phenomena. In the case of heterointerfaces based on SrTiO$_3$, many of these phenomena can be effectively tuned by using an electric gate, due to the large dielectric constant of SrTiO$_3$. Most studies so far have focused on (001) oriented heterostructures; however, (111) oriented heterostructures have recently gained attention due to the possibility of finding exotic physics in these systems due their hexagonal surface crystal symmetry. In this work, we use magnetoresistance to study the evolution of spin-orbit interaction and magnetism in a new system, (111) oriented (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)/SrTiO$_3$. At more positive values of the gate voltage, which correspond to high carrier densities, we find that transport is multiband, and dominated by high mobility carriers with a tendency towards weak localization. At more negative gate voltages, the carrier density is reduced, the high mobility bands are depopulated, and weak antilocalization effects begin to dominate, indicating that spin-orbit interaction becomes stronger. At millikelvin temperatures, and gate voltages corresponding to the strong spin-orbit regime, we observe hysteresis in magnetoresistance, indicative of ferromagnetism in the system. Our results suggest that in the (111) (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)/SrTiO$_3$ system, low mobility carriers which experience strong spin-orbit interactions participate in creating magnetic order in the system.